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Let alpha, beta be the roots of the equa...

Let `alpha, beta` be the roots of the equation `x^2 - 4lambda x + 5= 0 and alpha, gamma` be the roots of the equation `x^2- (3sqrt2 + 2sqrt3) x + 7 + 3lambda sqrt3 = 0, lambda gt 0. " If " beta + gamma = 3 sqrt2` , then `(alpha + 2beta + gamma)^2`is equal to _________.

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